A £25,000 reward has been offered for information about two thefts and one attempted theft over six days in November.
On two of the occasions, a stolen JCB digger was used to rip the machine from the wall.
The reward is being offered by the LINK Scheme, which manages the UK's cash machine network.
On 16 November, thieves used a digger to steal the cash machine from the Waitrose store in St Bernard Paget Avenue, in Ashford.
Three days later thieves attempted to steal a cash machine from the Natwest Bank, in High Street, Snodland. They abandoned their attempt after being disturbed by police and left the digger still holding the machine.
And on 22 November, a cash machine from the Co-op store in Newington High Street, Sittingbourne, was stolen. It was later found abandoned but intact.
Det Chief Inspector Keith Davies, of the Kent and Essex Serious Crime Directorate, said: "The theft of cash machines is a national problem - it is not unique to Kent, and police have been working for some time with the industry to improve security measures which make the machines more difficult to steal and easier to track if taken.
"Police have also talked to building firms about ways in which they can ensure plant machinery is secured to reduce the opportunity for thieves to use them in an attempt to steal cash machines."